First order Taylor and ordinary point series

2.8.1 First order Taylor and ordinary point series

Table 2.1257: First order Taylor and ordinary point [147]


#	ODE	solved	Maple	Mma	Sympy	time(sec)

400	\begin{align} y^{\prime }&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.332

401	\begin{align} y^{\prime }&=4 y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.381

402	\begin{align} 2 y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.378

403	\begin{align} y^{\prime }+2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.388

404	\begin{align} y^{\prime }&=y x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371

405	\begin{align} \left (x -2\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.394

406	\begin{align} \left (2 x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.411

407	\begin{align} 2 \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.399

408	\begin{align} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398

409	\begin{align} 2 \left (x -1\right ) y^{\prime }&=3 y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.397

424	\begin{align} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.246

1042	\begin{align} y^{\prime }&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.321

1043	\begin{align} y^{\prime }&=4 y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.351

1044	\begin{align} 2 y^{\prime }+3 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.357

1045	\begin{align} y^{\prime }+2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368

1046	\begin{align} y^{\prime }&=x^{2} y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371

1047	\begin{align} \left (x -2\right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.371

1048	\begin{align} \left (2 x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.378

1049	\begin{align} 2 \left (x +1\right ) y^{\prime }&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.376

1050	\begin{align} \left (x -1\right ) y^{\prime }+2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.375

1051	\begin{align} 2 \left (x -1\right ) y^{\prime }&=3 y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.372

1396	\begin{align} y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.286

1397	\begin{align} y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326

1398	\begin{align} \left (1-x \right ) y^{\prime }&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.333

3334	\begin{align} y^{\prime }&=\sqrt {1-y} \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.207

3335	\begin{align} y^{\prime }&=y x -x^{2} \\ y \left (0\right ) &= 2 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.449

3336	\begin{align} y^{\prime }&=x^{2} y^{2} \\ y \left (1\right ) &= 0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.279

3337	\begin{align} y^{\prime }&=3 x +\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.410

3338	\begin{align} y^{\prime }&=\ln \left (y x \right ) \\ y \left (1\right ) &= 1 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.374

3339	\begin{align} y^{\prime }&=1+y^{2} \\ y \left (1\right ) &= -1 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.270

3340	\begin{align} y^{\prime }&=x^{2}+y^{2} \\ y \left (2\right ) &= 0 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	0.315

3341	\begin{align} y^{\prime }&=\sqrt {y x +1} \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.231

3342	\begin{align} y^{\prime }&=\cos \left (x \right )+\sin \left (y\right ) \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align} Series expansion around \(x=\frac {\pi }{2}\).	✓	✓	✓	✓	0.747

7362	\begin{align} y^{\prime }&=3 x^{2} y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398

7631	\begin{align} y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.468

7632	\begin{align} y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.359

7633	\begin{align} z^{\prime }-x^{2} z&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.474

7645	\begin{align} y^{\prime }+2 \left (x -1\right ) y&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.472

7646	\begin{align} y^{\prime }-2 y x&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.533

7651	\begin{align} x^{\prime }+\sin \left (t \right ) x&=0 \\ x \left (0\right ) &= 1 \\ \end{align} Series expansion around \(t=0\).	✓	✓	✓	✓	0.540

7652	\begin{align} y^{\prime }-y \,{\mathrm e}^{x}&=0 \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.502

7656	\begin{align} y^{\prime }-y x&=\sin \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.523

7657	\begin{align} w^{\prime }+w x&={\mathrm e}^{x} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.563

8067	\begin{align} \left (1-x \right ) y^{\prime }&=x^{2}-y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.401

8068	\begin{align} x y^{\prime }&=1-x +2 y \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✗	0.438

8070	\begin{align} y^{\prime }&=2 x^{2}+3 y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.480

8071	\begin{align} \left (x +1\right ) y^{\prime }&=x^{2}-2 x +y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.393

8116	\begin{align} y^{\prime }+y x&=\cos \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.474

8125	\begin{align} y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366

8566	\begin{align} \left (x +1\right ) y^{\prime }&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.385

8567	\begin{align} y^{\prime }&=-2 y x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.459

8575	\begin{align} y^{\prime }+4 y&=1 \\ y \left (0\right ) &= {\frac {5}{4}} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.467

8578	\begin{align} \left (x -2\right ) y^{\prime }&=y x \\ y \left (0\right ) &= 4 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.546

9347	\begin{align} y^{\prime }&=2 y x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.601

9349	\begin{align} y^{\prime }+y&=1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.506

9351	\begin{align} y^{\prime }-y&=2 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.537

9353	\begin{align} y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.459

9355	\begin{align} y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.469

9357	\begin{align} y^{\prime }-y&=x^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.559

9366	\begin{align} y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.694

9367	\begin{align} y^{\prime }&=y+1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.516

9368	\begin{align} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.638

9487	\begin{align} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.390

9489	\begin{align} y^{\prime }-2 y&=x^{2} \\ y \left (1\right ) &= 1 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.681

9491	\begin{align} y^{\prime }&=y+x \,{\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✗	✓	0.990

10346	\begin{align} y^{\prime }+2 y x&=x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.437

10347	\begin{align} y^{\prime }+y&=\sin \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.458

16820	\begin{align} y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.431

16821	\begin{align} y^{\prime }-2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.412

16822	\begin{align} y^{\prime }+\frac {2 y}{2 x -1}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.441

16823	\begin{align} \left (x -3\right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.389

16824	\begin{align} \left (x^{2}+1\right ) y^{\prime }-2 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.382

16825	\begin{align} y^{\prime }+\frac {y}{x -1}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.434

16826	\begin{align} y^{\prime }+\frac {y}{x -1}&=0 \\ \end{align} Series expansion around \(x=3\).	✓	✓	✓	✓	0.514

16827	\begin{align} \left (1-x \right ) y^{\prime }-2 y&=0 \\ \end{align} Series expansion around \(x=5\).	✓	✓	✓	✓	0.489

16828	\begin{align} \left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.488

16829	\begin{align} \left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.438

16830	\begin{align} \left (x +1\right ) y^{\prime }-y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.467

16831	\begin{align} \left (x +1\right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.479

16853	\begin{align} y^{\prime }+\cos \left (y\right )&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.338

16854	\begin{align} y^{\prime }-y \,{\mathrm e}^{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.520

16855	\begin{align} y^{\prime }-y \tan \left (x \right )&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.589

16864	\begin{align} y^{\prime }-y \,{\mathrm e}^{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.464

16865	\begin{align} y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.524

16866	\begin{align} y^{\prime }+\cos \left (x \right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.500

16867	\begin{align} y^{\prime }+y \ln \left (x \right )&=0 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✗	0.640

16874	\begin{align} y^{\prime }-y \,{\mathrm e}^{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.786

16875	\begin{align} y^{\prime }+y \sqrt {x^{2}+1}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.076

16876	\begin{align} \cos \left (x \right ) y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.115

16877	\begin{align} y^{\prime }+\sqrt {2 x^{2}+1}\, y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.993

18371	\begin{align} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.573

18372	\begin{align} y^{\prime }&=\frac {-x +y}{x +y} \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✗	✓	0.398

18373	\begin{align} y^{\prime }&=y \sin \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.779

18379	\begin{align} y^{\prime }-2 y x&=0 \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.619

18385	\begin{align} y^{\prime }&={\mathrm e}^{y}+y x \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✗	✓	0.459

18387	\begin{align} \left (x +1\right ) y^{\prime }-n y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.662

19578	\begin{align} y^{\prime }&=2 y x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.421

19579	\begin{align} y^{\prime }+y&=1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.362

19582	\begin{align} y^{\prime }&=1+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.236

19583	\begin{align} y^{\prime }&=x -y \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.423

20881	\begin{align} y^{\prime }&=y \\ y \left (0\right ) &= 2 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.398

20882	\begin{align} y^{\prime }&=2 y x -x^{3} \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.498

20883	\begin{align} \left (x +1\right ) y^{\prime }&=y p \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.382

20884	\begin{align} y^{\prime }&=\sqrt {x^{2}+y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.391

20886	\begin{align} y^{\prime }&=-x +y \\ y \left (0\right ) &= 2 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.444

20887	\begin{align} \left (x +1\right ) y^{\prime }&=y p \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.378

20986	\begin{align} y^{\prime }&={\mathrm e}^{x}+x \cos \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	1.331

20987	\begin{align} y^{\prime }&=x^{3}+y^{3} \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.293

20988	\begin{align} u^{\prime }&=u^{3} \\ u \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.253

21637	\begin{align} y^{\prime }-y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.454

21644	\begin{align} y^{\prime }&=x^{2} \\ y \left (2\right ) &= 1 \\ \end{align} Series expansion around \(x=2\).	✓	✓	✓	✓	0.550

21645	\begin{align} y^{\prime }&=y \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.461

21665	\begin{align} x^{\prime }+x^{2}&=0 \\ x \left (-\frac {1}{2}\right ) &= 0 \\ \end{align} Series expansion around \(t=-{\frac {1}{2}}\).	✓	✓	✓	✓	0.320

21906	\begin{align} y^{\prime }-y^{2}-x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.434

22821	\begin{align} y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.660

22822	\begin{align} y^{\prime }&=y x \\ y \left (0\right ) &= 5 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.793

22823	\begin{align} y^{\prime }&=2 x -y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.822

22838	\begin{align} y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.655

22839	\begin{align} y^{\prime }+y&=x^{2} \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.846

22840	\begin{align} y^{\prime }&=y+{\mathrm e}^{x} \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.742

22841	\begin{align} 2 y^{\prime }+y x -y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.817

23450	\begin{align} y^{\prime }+3 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.417

23666	\begin{align} y^{\prime }&=3 y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.368

24080	\begin{align} \left (-x^{2}+1\right ) y^{\prime }+3 y x&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.450

24115	\begin{align} y^{\prime }&=2 y \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.432

24116	\begin{align} y^{\prime }&=x +2 y \\ y \left (0\right ) &= 2 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.427

24117	\begin{align} y^{\prime }-y&=x^{2}+1 \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.404

24118	\begin{align} y^{\prime }-y&=x^{2}+1 \\ y \left (0\right ) &= -3 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.447

24119	\begin{align} y^{\prime }-7 y&=-x^{4}+2 \\ y \left (0\right ) &= a \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.483

26705	\begin{align} y^{\prime }-2 y x&=0 \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.487

26706	\begin{align} 4 x y^{\prime }+2 y^{\prime }+y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.298

26707	\begin{align} \left (x +1\right ) y^{\prime }-n y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.270

26714	\begin{align} y^{\prime }&=x^{2}+y^{2} \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.229

26715	\begin{align} y^{\prime }&={\mathrm e}^{y}+y x \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.366

27062	\begin{align} y^{\prime }-y x&=1-x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.422

27063	\begin{align} y^{\prime }-x^{3} y&=4 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.369

27064	\begin{align} y^{\prime }+\left (-x^{2}+1\right ) y&=x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.471

27753	\begin{align} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.370

27754	\begin{align} y^{\prime }&=x +\frac {1}{y} \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.256

27755	\begin{align} y^{\prime }&=y+x \,{\mathrm e}^{y} \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.442

27756	\begin{align} y^{\prime }&=2 x +\cos \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.617

27757	\begin{align} y^{\prime }&=x^{2}+y^{3} \\ y \left (1\right ) &= 1 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.336

27760	\begin{align} y^{\prime }&=y^{2}-x \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.134

27761	\begin{align} y^{\prime }&={\mathrm e}^{y}-x^{2} y \\ y \left (0\right ) &= 0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.322

27784	\begin{align} y^{\prime }&=4 \mu \left (x +1\right )-y^{2} \\ y \left (0\right ) &= 1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✓	0.136

27785	\begin{align} y^{\prime }&=\frac {2}{y}-5 \mu x \\ y \left (1\right ) &= 2 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.254

27786	\begin{align} x y^{\prime }&=x^{2} \mu +\ln \left (y\right ) \\ y \left (1\right ) &= 1 \\ \end{align} Series expansion around \(x=1\).	✓	✓	✓	✓	0.425

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